# Polynomial help?

• Oct 23rd 2008, 06:32 AM
kim_lloyd25
Polynomial help?
Hey!
Im going through some polynomial questions as revision but i've come across one that's stumped me. I've tried it over and over but just can't see where i'm going wrong. The question is as follows:

The polynomial: f(x)= px^3 - x^2 + qx - 6
has x-3 as a factor. When f(x) is divided by x-2, the remainder in -20.

(a) Show that p=2 and find the value of q
(b) Factorise f(x)

For the first part i've come out with p=2, which is right, and q=-13. However, this doesn't factorise well in the second part.
Any help would be great! Thanks for reading! (Hi)
• Oct 23rd 2008, 07:06 AM
masters
Quote:

Originally Posted by kim_lloyd25
Hey!
Im going through some polynomial questions as revision but i've come across one that's stumped me. I've tried it over and over but just can't see where i'm going wrong. The question is as follows:

The polynomial: f(x)= px^3 - x^2 + qx - 6
has x-3 as a factor. When f(x) is divided by x-2, the remainder in -20.

(a) Show that p=2 and find the value of q
(b) Factorise f(x)

For the first part i've come out with p=2, which is right, and q=-13. However, this doesn't factorise well in the second part.
Any help would be great! Thanks for reading! (Hi)

Everything looks good to me. After dividing by (x-3), you're left with

\$\displaystyle 2x^2+5x+2\$, which factors into \$\displaystyle (2x-1)(x+2)\$